Would you want a turboprop for those speeds, or infernal combustion engine? How would a brand new designed and optimized infernal combustion engine compare against turbine?
I think in general power requirements >500 hp favor turbines. I read theoretically they could be ~ 20 % more fuel efficient then turbines.
A infernal combustion engines would weigh a lot more however, requiring a heavier wing, orsionbox, landinggear etc. and it would be a challenge to make as reliable as a turbine. (lots of moving parts, resonance)
Dryweight of a RR Griffon is 900kg, a PW100 about half (450kg) Add up all additional structure. The more efficient fuel consumption would have to compensate the weight on high frequency short trips..
But I'm not aware of the latest development in this area (couldn't fin a new high powered cilinder engine..